PSN THAP068
PULSED ELECTRON SOURCE CHARACTERIZATION WITH THE
MODIFIED THREE GRADIENT METHOD
S. Marghitu, C.Oproiu, NILPRP, Acc. Lab., Bucharest−Magurele, R−76900, Romania
D. C. Dinca, MSU−NSCL, East Lansing, MI 48824−1321, USA
O. Marghitu, NILPRP − ISS, Bucharest−Magurele, R−76900, Romania
Abstract
Results from the Modified Three Gradient Method
(MTGM), applied to a pulsed high intensity electron
source, are presented. The MTGM makes possible the
non−destructive determination of beam emittance in
the space charge presence [1]. We apply the MTGM
to an experimental system equipped with a Pierce
convergent diode, working in pulse mode, and having
a directly heated cathode as electron source. This
choice was mainly motivated by the availability of an
analytical characterization of this source type [2], as
well as the extended use of the Pierce type sources in
linear accelerators. The experimental data are
processed with a numerical matching program, based
on the K−V equation for an axially symmetric
configuration [3], to determine the emittance and
object cross−over position and diameter. The variation
of these parameters is further investigated with respect
to both electrical and constructive characteristics of
the source: cathode heating current, extraction
voltage, and cathode−anode distance.
1 INTRODUCTION
Non−destructive measurements of emittance and
object cross−over radius and position, for a pulsed
high intensity electron source, are presented. Our goal
is to check the possibility of using MTGM as a
reliable routine tool in beam diagnosis.
The MTGM, [1], is based on three gradient type
measurements of the beam cross−section and on the
subsequent use of a computer code incorporating the
K−V equation. The experimental installation built up
to set and check the method is shown as Figure 1.
2 THEORETICAL BACKGROUND
The envelope of an axially symmetric beam,
propagating in an electric field free region, in paraxial
approximation, follows the equation (e.g. [3]):
d2R η B2
1
I 1 ε2
+
R
=
+
2
8V
4πε 0 V 3 / 2 R R 3
dz
(1)
Figure 1: Experimental set−up
a − beam system; b − vacuum installation; c − pulse
high voltage transformer. The beam system consists
of: S − the electron source; L − thin, axially
symmetric, magnetic lens; M1, M2 − beam profile
monitors (BPM); VR − vacuum room, with a specially
designed Faraday cup inside
where: η = charge−to−mass ratio for the electron, ε0 =
dielectric constant, I = beam current, V = beam
acceleration potential, ε = beam emittance (which
according to Liouville’s theorem remains constant), R
= beam envelope, and B = axial magnetic field.
To solve equation (1) is necessary to know the
parameters I, V, B, and ε, as well as some initial
conditions. It turns out that only ε requires a special
effort to be determined; I and V can be directly
measured, whereas B=B(z) depends on the geometry
of the lens and on its polarization, and can be
calculated with dedicated software.
The initial conditions are also unknown. A good
choice for us is the distance of the object cross−over
from the center of the focusing lens L, z0, and its
radius, R0. Consequently, to get the evolution of the
beam, one has to find (ε, z0, R0).
3 MEASUREMENTS
As already mentioned, V and I are measured
directly, by using a two channel digital oscilloscope.
An example oscillogram is given here as Figure 2.
The ’shorter’ pulse is the current, I, at M1 exit plane,
measured on a 1Ω resistor, while the ’longer’ one is
the high−voltage, V. For the example shown
V=31.7kV, I=0.43A. The corresponding cathode
heating current and lens polarization voltage are
Ifil=8.4A and UL=4.4V.
Before proceeding to beam cross−section
measurements, the volt−ampere characteristics of the
source was obtained, for two different geometries, IG
(initial geometry) and MG (modified geometry). For
IG the distance between the anode tip and the
emissive filament is dac1 =19mm, whereas for MG dac2
=22mm. The oscillogram in figure 2 corresponds to
geometry IG. The function I=I(V,Ifil) is tabulated
below, in Tables 1 and 2, for respectively IG and MG.
Table 1− Current beam I [A] at anode exit for IG.
V[kV]
9.3
18.6
27.9
37.2
46.5 55.8
Ifil [A]
8.1
0.13 0.228
0.264
0.284
0.3
0.32
8.6
0.15
0.38
0.5
0.536 0.61 0.63
9.1
0.2
0.48
0.712
0.96
1.1 1.18
9.5
−
0.484
0.8
1.16
1.5
1.7
Figure 2: Oscillogram of V (’longer’ pulse) and I
(’shorter’ pulse) at M1 exit plane; Ifil=8.4A, UL =4.4V
with polynomials (3 to 5 degree), and the coefficients
fed to the computer code MTGMprog, developed to
assist MTGM. The program is based on a Monte Carlo
algorithm that searches the (ε, z0, R0) parameter space,
until the best fit to the data, within a given error, is
found. A typical result is given in the next section, as
figure 7.
Table 2− Current beam I [A] at anode exit for MG
V[kV]
10.4
15.6
20.8 26.0 31.6 36.4
Ifil [A]
8.4
0.102
0.168
0.22 0.26 0.32 0.33
8.6
0.11
0.19
0.24 0.31 0. 37 0.44
8.8
0.114
0.198
0.28 0.35 0.42
0.5
9.1
0.116
0.2
0.29 0.39 0.46
0.6
Determination of the beam diameter is the most
sensible part of the measurements, [4]. Each BMP
consists of wire scanner that crosses the beam at
constant velocity, vM. The diameter results by
multiplying the velocity with the scanning time, τM, as
read with a second oscilloscope. The measurements
have to be conducted with great care, because of
various potential error sources; in particular, for the
low energy range emphasized here, the backscattered
electrons can seriously alter the data. Upper part of
figure 3 shows the pulses obtained when a diaphragm
in front of the Faraday cup is placed too close to M1;
lower part of the figure shows the effect of removing
the diaphragm. These data correspond again to
geometry IG.
For each case studied the beam radii, R1 and R2,
are measured as function of the lens polarization
voltage, UL. The experimental values are then fitted
Figure 3: Effect of the back−scattered electrons on
the beam cross−section determination
Eps, Epsn [mm.mrad]
Figure 4: Emittance variation for IG; Ifil =ct=8.4A;
I1, I2, I3 are: 0.32A, 0.41A, 0.46A
1
140
130
EpsGI
EpsnGI
2
120
5
Linear fit
2
4
Experimental variation
Linear fit
16
20
24
28
32
36
40
Ui −kV
24
22
RM1T
RM2T
RM1Ex
RM2Ex
18
16
100
90
Experimental Variation
14
3
80
4
12
70
10
60
8
50
Linear fit
40
6
30
4
Experimental variation
20
2
10
0
0.36
EpsMG1
EpsnMG1
20
Linear fit
110
1 Experimental variation
3
Figure 6: Emittance variation for MG; Ifil =ct=8.4A;
I1, I2, I3, I4, I5 are: 0.19A, 0.26A, 0.34A, 0.42A, 0.52A
R [ mm]
Eps, Epsn [ mm.mrad ]
150
60
56
52
48
44
40
36
32
28
24
20
16
12
8
4
0
12
0
0.40
0.44
0.48
0.52
0.56
0.60
0.64
2.4
2.8
3.2
3.6
4.0
4.4
4.8
5.2
5.6
6.0
6.4
6.8
7.2
Ub −V
If [ A ]
Figure 5: Emittance variation for IG; V=ct=31.6kV;
Ifil1, Ifil2, Ifil3, Ifil4 are: 8.4A, 8.5A, 8.6A, 8.7A
Figure 7: Beam radii R1, R2 dependence on UL;
experimental measurement vs. numerical fit
4 RESULTS
R0=1.71mm, z0=73.8mm. The good match between
the measured and calculated values is evident.
To conclude, we consider the results presented
here as very promising. Further work is needed to
improve the computing code, as well as for
accumulating a better case statistics.
The dependence of the emittance, ε, on V and Ifil,
for the geometry IG, is shown in figures 4 and 5 (note
that in figure 5 the beam current, I, is used for the
abscissa). In particular, figure 5 corresponds to the
usual case in linear electron accelerators, with V fixed
by design. One can see that the variation of the
normalized emittance, εn, is rather small, in agreement
with the theory. Another observation refers to the
relatively linear variation of ε with respect to both
parameters, which makes possible the use of a linear
fit, once a few experimental poins were determined.
Figure 6 presents the dependence of ε on V for the
geometry MG. The most pregnant feature, compared
to figure 4, is the large variation (~300%) for a
relatively small (~16%) change in the anode−cathode
distance. This variation is in the expected sense: the
larger is the distance dac, the more uniform is the
electric field in between and smaller the ε. The
variation of εn is again small, and the trend linear,
although this time there is a significant scatter of the
points. This is probably related to the computing code.
Because of lack of space we cannot show here
graphs with the variation of the object cross−over
position and radius, z0 and R0. However, consistency
checks between the measured and calculated data
were performed. An example is shown in figure 7,
that corresponds to point 2 in figure 4. For this case
Acknowledgment: Work supported by the Romanian
Ministry of Education and Research, grant
3216C/2000.
REFERENCES
[1] S. Marghitu, C. Dinca, M. Rizea, C. Oproiu, M.
Toma, D. Martin, E. Iliescu, “Non−destructive
beam characterization at an Electron Source
Exit”, Nucl. Instr. Meth. In Phys. Research B,
161−163, pp. 1113−1117, 2000.
[2] J.R. Pierce, “Theory and design of electron
beams”, 2nd ed.., Van Nostrand., 1954.
[3] P.Ciuti, "On the equation defining the profile of
Non−relativistic beams with space charge forces
and finite emittance”, Nucl.Instr.Meth. 93,
pp. 295−299, 1971.
[4] C Bonnafond, E Merle, J. Bardy, A. Devin, C.
Vermare, D. Villate, "Optical and time−resolved
diagnostics for the AIRIX high current electron
beam", Proc. 3rd European Workshop DIPAC97,
pp 156−158, 1997.